Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg(\frac{(1 + x)}{lg(1 - x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})\right)}{dx}\\=&\frac{(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{ln{10}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})}\\=&\frac{1}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{1}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln{10}lg(-x + 1)} + \frac{x}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{1}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln{10}lg(-x + 1)} + \frac{x}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)}\right)}{dx}\\=&\frac{(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)ln^{2}{10}lg^{2}(-x + 1)} + \frac{-2*0}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{-2(-1 + 0)}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} + \frac{(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{ln{10}lg(-x + 1)} + \frac{-0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg(-x + 1)} + \frac{-(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln{10}lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{(\frac{-(-1 + 0)}{(-x + 1)^{2}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})x}{(-x + 1)ln^{2}{10}lg^{2}(-x + 1)} + \frac{1}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{x*-2*0}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{x*-2(-1 + 0)}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)}\\=&\frac{1}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{1}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{2}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} - \frac{1}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln{10}lg^{2}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} + \frac{2}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{2x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{1}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{2}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} - \frac{1}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln{10}lg^{2}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} + \frac{2}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{2x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)}\right)}{dx}\\=&\frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{2}ln^{2}{10}lg^{2}(-x + 1)} + \frac{-2*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{-2(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{2(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{3}{10}lg^{3}(-x + 1)} - \frac{2*-3(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2x*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{2x*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{2}ln^{3}{10}lg^{3}(-x + 1)} + \frac{2*-3*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{3}(-x + 1)} + \frac{2*-3(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{ln{10}lg^{2}(-x + 1)} - \frac{-0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{2}(-x + 1)} - \frac{-2(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln{10}lg^{3}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{2x*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{3}{10}lg^{3}(-x + 1)} - \frac{2x*-3(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{2(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)ln^{2}{10}lg^{2}(-x + 1)} + \frac{2*-2*0}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{2*-2(-1 + 0)}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} + \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})x}{(-x + 1)^{2}ln^{2}{10}lg^{2}(-x + 1)} + \frac{1}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{x*-2*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{x*-2(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x^{2}}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{x^{2}*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{x^{2}*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})x}{(-x + 1)^{2}ln^{3}{10}lg^{3}(-x + 1)} + \frac{2}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2x*-3*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{3}(-x + 1)} + \frac{2x*-3(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{4}(-x + 1)ln{10}(-x + 1)}\\=&\frac{2}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{1}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{1}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{6}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} + \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} + \frac{12x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} - \frac{2}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{10}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{6x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} - \frac{12x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} + \frac{6}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} + \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln{10}lg^{3}(-x + 1)} + \frac{6x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} - \frac{2}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{4}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{8x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{3}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{6}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} - \frac{4x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{5x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{3x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} + \frac{6x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{6x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} + \frac{2x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{6x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{1}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{1}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{6}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} + \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} + \frac{12x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} - \frac{2}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{10}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{6x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} - \frac{12x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} + \frac{6}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} + \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln{10}lg^{3}(-x + 1)} + \frac{6x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} - \frac{2}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{4}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{8x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{3}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{6}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} - \frac{4x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{5x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{3x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} + \frac{6x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{6x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} + \frac{2x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{6x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)}\right)}{dx}\\=&\frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{2(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{3}ln^{2}{10}lg^{2}(-x + 1)} + \frac{2*-2*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{2*-2(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{-3*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{-4(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{-2*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{3}(-x + 1)} - \frac{-3(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{1}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{x*-3*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{x*-4(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{6(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{3}ln^{3}{10}lg^{3}(-x + 1)} + \frac{6*-3*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{3}(-x + 1)} + \frac{6*-3(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})}{(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{2*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{5}{10}lg^{6}(-x + 1)} + \frac{2*-6(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})}{(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{4}{10}lg^{5}(-x + 1)} + \frac{6*-5(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{6}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})x}{(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6x*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{5}{10}lg^{6}(-x + 1)} + \frac{6x*-6(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{4}(-x + 1)} - \frac{2*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{6(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} - \frac{6*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{5}{10}lg^{5}(-x + 1)} - \frac{6*-5(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})}{(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} + \frac{6(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{2}{10}lg^{4}(-x + 1)} + \frac{6*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{3}{10}lg^{4}(-x + 1)} + \frac{6*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{12(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})x}{(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{12(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{12}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{12x*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{4}{10}lg^{5}(-x + 1)} + \frac{12x*-5(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{6}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{2*-3*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{2*-4(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{10(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{10(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{10*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{10*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})x^{2}}{(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6*2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{6x^{2}*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{5}{10}lg^{6}(-x + 1)} + \frac{6x^{2}*-6(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})x^{2}}{(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6*2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{6x^{2}*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{4}{10}lg^{5}(-x + 1)} + \frac{6x^{2}*-5(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{6}(-x + 1)ln{10}(-x + 1)} - \frac{12(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{12(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} - \frac{12}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{12x*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{5}{10}lg^{5}(-x + 1)} - \frac{12x*-5(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{3}(-x + 1)} - \frac{2*-3(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} + \frac{6(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{3}ln^{4}{10}lg^{4}(-x + 1)} + \frac{6*-4*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{5}{10}lg^{4}(-x + 1)} + \frac{6*-4(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})}{ln{10}lg^{3}(-x + 1)} + \frac{2*-0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{2}{10}lg^{3}(-x + 1)} + \frac{2*-3(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln{10}lg^{4}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})x}{(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} + \frac{6(\frac{-(-1 + 0)}{(-x + 1)^{2}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{2}{10}lg^{4}(-x + 1)} + \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} + \frac{6x*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{3}{10}lg^{4}(-x + 1)} + \frac{6x*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{2*-2*0}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{3}(-x + 1)} - \frac{2*-3(-1 + 0)}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{1}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{x*-2*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{3}(-x + 1)} - \frac{x*-3(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{4(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})}{(-x + 1)ln^{2}{10}lg^{3}(-x + 1)} - \frac{4(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{4*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{3}{10}lg^{3}(-x + 1)} - \frac{4*-3(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{8(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{8(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{8}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{8x*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{8x*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{3(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{3(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{2}ln^{2}{10}lg^{2}(-x + 1)} + \frac{3*-2*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{3*-2(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{6(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})}{(-x + 1)^{2}ln^{3}{10}lg^{3}(-x + 1)} + \frac{6*-3*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{3}(-x + 1)} + \frac{6*-3(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{4(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{4(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{4}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{4x*-3*0}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{4}(-x + 1)} - \frac{4x*-4(-1 + 0)}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{5(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{5(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{5}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{5x*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{4}(-x + 1)} - \frac{5x*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} - \frac{2(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x}{(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{2x*-2*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{3}(-x + 1)} - \frac{2x*-3(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} - \frac{3(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x^{2}}{(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{3(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{3*2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{3x^{2}*-3*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{4}(-x + 1)} - \frac{3x^{2}*-4(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{5}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{6(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})x}{(-x + 1)^{3}ln^{3}{10}lg^{3}(-x + 1)} + \frac{6}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{6x*-3*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{3}(-x + 1)} + \frac{6x*-3(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{4}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-3(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}})x^{3}}{(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{2*3x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{2x^{3}*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{5}{10}lg^{6}(-x + 1)} + \frac{2x^{3}*-6(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)ln{10}(-x + 1)} - \frac{6(\frac{-2(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}})x^{2}}{(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} - \frac{6*2x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{6x^{2}*-4*0}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{5}{10}lg^{5}(-x + 1)} - \frac{6x^{2}*-5(-1 + 0)}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)ln{10}(-x + 1)} + \frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{2(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})x}{(-x + 1)^{3}ln^{2}{10}lg^{2}(-x + 1)} + \frac{2}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} + \frac{2x*-2*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{2}(-x + 1)} + \frac{2x*-2(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{3}(-x + 1)ln{10}(-x + 1)} + \frac{6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} + \frac{6(\frac{-(\frac{-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)} + \frac{1}{lg(-x + 1)} + \frac{x*-(-1 + 0)}{lg^{2}(-x + 1)ln{10}(-x + 1)})}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}})x}{(-x + 1)^{3}ln^{4}{10}lg^{4}(-x + 1)} + \frac{6}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} + \frac{6x*-4*0}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{5}{10}lg^{4}(-x + 1)} + \frac{6x*-4(-1 + 0)}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{5}(-x + 1)ln{10}(-x + 1)}\\=&\frac{6}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{5}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{4}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{7x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{22}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} + \frac{2}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{2}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{36}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{2}ln^{3}{10}lg^{6}(-x + 1)} + \frac{4x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{10}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} + \frac{2}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{2}{10}lg^{4}(-x + 1)} + \frac{22}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{3}{10}lg^{5}(-x + 1)} - \frac{14}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{46x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{2x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} - \frac{72x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{2}ln^{3}{10}lg^{6}(-x + 1)} + \frac{2x^{2}}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{16x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} - \frac{24}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)ln^{2}{10}lg^{5}(-x + 1)} + \frac{4}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{36}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} - \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{4}ln^{5}{10}lg^{8}(-x + 1)} - \frac{24}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)} - \frac{24x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{4}ln^{5}{10}lg^{8}(-x + 1)} + \frac{10}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{4}{10}lg^{6}(-x + 1)} + \frac{24}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{5}{10}lg^{7}(-x + 1)} - \frac{72x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)} + \frac{72}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{36x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{4}ln^{5}{10}lg^{8}(-x + 1)} - \frac{72x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)} + \frac{72x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{5}{10}lg^{7}(-x + 1)} + \frac{32x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{4}{10}lg^{6}(-x + 1)} - \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{3}{10}lg^{4}(-x + 1)} - \frac{26}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{4}{10}lg^{5}(-x + 1)} - \frac{30}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{5}{10}lg^{6}(-x + 1)} + \frac{68}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} + \frac{10}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{2}{10}lg^{4}(-x + 1)} - \frac{36x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{2}ln^{3}{10}lg^{6}(-x + 1)} + \frac{132x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{14}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} - \frac{34}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} - \frac{58}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} - \frac{24x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{3}ln^{4}{10}lg^{7}(-x + 1)} - \frac{24x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{4}ln^{5}{10}lg^{8}(-x + 1)} + \frac{34x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{4}{10}lg^{6}(-x + 1)} + \frac{12x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{72x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{5}{10}lg^{7}(-x + 1)} + \frac{24x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{20x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{3}{10}lg^{5}(-x + 1)} + \frac{66x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{3}ln^{4}{10}lg^{6}(-x + 1)} - \frac{56x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{4}{10}lg^{5}(-x + 1)} - \frac{60x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{5}{10}lg^{6}(-x + 1)} - \frac{4}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{2}{10}lg^{3}(-x + 1)} - \frac{6}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{5}{10}lg^{6}(-x + 1)} - \frac{12x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{5}{10}lg^{6}(-x + 1)} + \frac{24}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{5}{10}lg^{5}(-x + 1)} - \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}ln{10}lg^{4}(-x + 1)} - \frac{24x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)ln^{2}{10}lg^{5}(-x + 1)} + \frac{6}{(-x + 1)(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{2}{10}lg^{4}(-x + 1)} + \frac{2x}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{2}{10}lg^{4}(-x + 1)} + \frac{18}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)ln^{2}{10}lg^{4}(-x + 1)} + \frac{52x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{3}{10}lg^{5}(-x + 1)} - \frac{16}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{6}{(-x + 1)^{2}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{23x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{20}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{3}{10}lg^{4}(-x + 1)} + \frac{10x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{2}ln^{2}{10}lg^{4}(-x + 1)} - \frac{38x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{4}{10}lg^{5}(-x + 1)} + \frac{8}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{25x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{3}{10}lg^{4}(-x + 1)} + \frac{24}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} - \frac{6}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{2}ln^{2}{10}lg^{3}(-x + 1)} + \frac{24}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} - \frac{4x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{2}{10}lg^{3}(-x + 1)} - \frac{34x}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} - \frac{15x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{3}{10}lg^{4}(-x + 1)} - \frac{4x}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{3}ln^{2}{10}lg^{3}(-x + 1)} + \frac{12x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{4}{10}lg^{6}(-x + 1)} - \frac{9x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{3}{10}lg^{4}(-x + 1)} - \frac{30x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{4}{10}lg^{5}(-x + 1)} + \frac{22x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{3}{10}lg^{3}(-x + 1)} - \frac{6x^{2}}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{4}{10}lg^{5}(-x + 1)} + \frac{36x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{4}{10}lg^{4}(-x + 1)} - \frac{6x^{4}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{4}(-x + 1)^{4}ln^{5}{10}lg^{8}(-x + 1)} + \frac{6x^{2}}{(-x + 1)^{3}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}ln^{4}{10}lg^{6}(-x + 1)} + \frac{24x^{3}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{3}(-x + 1)^{4}ln^{5}{10}lg^{7}(-x + 1)} - \frac{30x^{2}}{(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}(-x + 1)^{4}ln^{5}{10}lg^{6}(-x + 1)} + \frac{6x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{2}{10}lg^{2}(-x + 1)} - \frac{2x^{2}}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{3}{10}lg^{4}(-x + 1)} - \frac{6x^{2}}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})^{2}ln^{5}{10}lg^{6}(-x + 1)} + \frac{24x}{(-x + 1)^{4}(\frac{1}{lg(-x + 1)} + \frac{x}{lg(-x + 1)})ln^{5}{10}lg^{5}(-x + 1)}\\ \end{split}\end{equation} \]